ON SOME PROPERTIES OF NORMAL Γ-IDEALS IN NORMAL Γ-SEMIGROUPS

Year 2019, Volume: 9 Issue: 3, 455 - 460, 01.09.2019

A. Basar M. Y. Abbasi

Abstract

We introduce the concept of normal T-ideal and bi-T-ideal in normal T- semigroups. We characterize the normal T-semigroup and normal regular T-semigroup in terms of elementary properties of bi-T-ideal proving the various equivalent conditions. In particular, we establish, among the other things, that if I1; I2 are any two normal T- ideals of a T-semigroup S, then their product I1TI2 and I2TI1 are also normal T-ideals of S and I1TI2 = I2TI1. Finally, we show that the minimal normal T-ideal of a T-semigroup S is a T-group.

Keywords

T-semigroup, normal ideal

References

• Funabashi, N. K., (1977), On Normal Semigroups, Czechoslovak Mathematical Journal, 27(1), 43-53.
• Howie, J., (1995), Fundamentals of semigroup theory, London Mathematical Society Monographs, New Series, 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York.
• Chattopadhyay, S. and Kar, S., (2008), On the structure space of Γ-semigroup, Acta Univ. Palacki
• Olomuc., Fac. rer. nat., Mathematica, 47, 37-46. Chattopadhyay, S., (2001), Right inverse Γ-semigroup, Bull. Cal. Math. Soc., 93(6), 435-442.
• Chattopadhyay, S., (2005), Right orthodox Γ-semigroup, Southeast Asian Bull. of Mathematics, 29, 30.
• Chinram, R. and Jirojkul, C., (2007), On bi-Γ-ideals in Γ-semigroups, Songklanakarin J. Sci. Technol., (1), 231-234.
• Lajos, S.,(1964), Note on (m,n)-ideals. II, Proc. Japan Acad., 40, 631-632.
• Petrich, M.,(1973), Introduction to Semigroups, Merill, Columbus.
• Sen, M. K. and Saha, N. K., (1986), On Γ-semigroup I, Bull. Calcutta Math. Soc., 78, 180-186.
• Sen, M. K., and Chattopadhyay, S.,(2004), Semidirect Product of a Monoid and a Γ-semigroup, East- West J. of Math., 6(2), 131-138.
• Sen, M. K. and Saha, N. K.,(1990), Orthodox Γ-semigroup, Internat. J. Math. Math. Sci., 13, 527-534.
• Sen, M. K., (1981), On Γ-semigroups, Proceedings of the International Conference on Algebra and its
• Applications, Dekker Publications, New York, 301-308. Saha, N. K., (1987), On Γ-semigroup II, Bull. Calcutta Math. Soc., 79, 331-335.
• Saha, N. K., (1988), On Γ-semigroup III, Bull. Calcutta Math. Soc., 80, 1-12.